Conventionally, the heat generation rate in a cylinder is approximated by the Wiebe function in order to express a combustion state of an internal combustion engine. With the Wiebe function, the heat generation rate waveform can be appropriately expressed by identifying a plurality of parameters. The Wiebe function is used for estimating the heat generation rate or the combustion mass rate due to combustion in the internal combustion engine.
For example, in a method for determining Wiebe function parameters described in Patent Document 1, a shape parameter m of the Wiebe function is identified by a predetermined expression based on a combustion rate at a crank angle where the heat generation rate is maximum. Other parameters such as k, a/θpm+1, and θb are also identified by the respective predetermined expressions, thus the Wiebe function can be determined so that it is adapted to an actual heat generation pattern with a high accuracy.
Patent Document 1 describes that, by determining the Wiebe function by identifying the plurality of parameters such as m, k, a/θpm+1, and θb under various operation conditions, it is possible to understand the relationships between the above parameters and operation parameters (e.g., the load rate, the rotation speed, the air-fuel ratio and the spark time) of the internal combustion engine. Thus, by using the relationships as understood above, it is possible to determine the Wiebe function under any operation condition of the internal combustion engine, which results in accurate expression of the combustion state of the internal combustion engine.